Question

O valor da expressão (1-√3) ÷ 2-√3 é:

a) -(1-√3)
b) -(1+√3)
c) 1+√3
d) 1-√3
e) -√3

Answer 1

Olá


Resposta correta, letra B) -(1+√3)




$\displaystyle \mathsf{ \frac{1- \sqrt{3} }{2- \sqrt{3} } }$


Multiplica a expressão pelo conjugado do denominador


$\displaystyle \mathsf{ \frac{1- \sqrt{3} }{2- \sqrt{3} } ~\cdot~ \frac{2+\sqrt{3}}{2+ \sqrt{3} } }\\\\\\\\\mathsf{ \frac{(1- \sqrt{3} )(2+ \sqrt{3} )}{2^2-( \sqrt{3} )^2} }\\\\\\\text{Cancela a raiz quadrada com o expoente}\\\\\\\mathsf{ \frac{(1- \sqrt{3} )(2+ \sqrt{3} )}{4-3} }\\\\\\\mathsf{(1- \sqrt{3} )(2+ \sqrt{3} )}$



Aplica a distributiva



$\displaystyle \mathsf{(1- \sqrt{3} )(2+ \sqrt{3})}\\\\\\\mathsf{2+\sqrt{3}-2\sqrt{3}-(\sqrt{3})^2}\\\\\\\mathsf{2+\sqrt{3}-2\sqrt{3}-3}\\\\\\\mathsf{-1-\sqrt{3}}$



Coloca o 'sinal negativo' em evidência

$\boxed{\mathsf{-(1+\sqrt{3})}}$



Letra B)